As established in Ref.[1]} these ModMax theories are the only NLE theories which preserve all the same symmetries as those of Maxwell linear
electrodynamics (recovered for \(\gamma =0\) ) — namely spacetime Poincaré and conformal invariance as is manifest from their Lagrangian density, as well as
duality invariance as is manifest from their Hamiltonian density — and which are continuous deformations of MLE. The only other such
electrodynamics theory sharing all these same symmetries is defined[1]} by the BB Hamiltonian density[3]}, \({\cal H}_{BB}=|\vec{D}\times \vec{B}|\) .
Note that \({\cal L}_\gamma \)  is nonanalytic in \(({\cal S},{\cal P})\)  at \(({\cal S},{\cal P})=(0,0)\)  for all \(\gamma \ne 0\) , namely for null \((\vec{E},\vec{B})\)  fields.
